Magyar nyelvű változat (Hungarian version)
MEK fejléc (Bibliographic data, in Hungarian)

### Barna Szénássy

## Contributions to the History of the Bolyai-Prize

Quite a few publications appeared lately dealing with the renewal of the former Bolyai-prize. These publications mention the initiative as an accomplished fact and describe the MTA's (Hungarian Academy of Sciences) aim regarding this matter. Academician Dénes Berényi puts it in a concise and clear way: "There are 2 contributing factors to the importance of the renewal of the prize. The MTA returns to a magnificent tradition, which honours worldwide scientific achievement, the scientific quality. The other - and not less important consequence - is that we are again looking out into the world. "[1]

Witnessing the noble intention of the MTA, which is on the verge of being realized I try to recall the beginnings around the turn of the century and I mention some pertinent data, which until now have not been available.

As it was first called "Bolyai-award ", its origins go back to the sixties of the last century. More precisely, it is about a session held in 1867, thus commented by the Bulletin of the Academy:

"Jenő Hunyady, corresponding member reports about a treatise published by the Academy of Bordeaux, entitled »La Science absolue de l'espace par J. Bolyai, précédée d'une notice sur la vie et les travaux de W. et de J. Bolyai, par F. Schmidt, architecte à Temesvár.« »The absolute science of the space by János Bolyai, with an introductory note about the life and work of F. and J. Bolyai, prepared by F. Schmidt, architect in Timisoara.« - The same individual proposes, that al1 the works of Farkas and János Bolyai, recognized Hungarian mathematicians throughout Europe should be requested for use by the MTA from the Tirgu Mures reformed college, where these works are kept."[2]

Without going into the already wellknown details as to the background of this report, the following can be said: Taking up the initiative of the prominent professor of mathematics G. J. Hoüel (1823-1886) in Bordeaux and that of the Italian G. Battaglini (1826-1894), the Appendix was published in French (1867) and in Italian (1868) completed by the biography of the 2 Bolyais, written by the untiring Hungarian Bolyai-researcher, Ferenc Schmidt (1827-1901). It is not my intention here to enlist all the relevant data, but let me mention, that J. Frischauf (1837-1924) professor of the University of Graz from 1871 on held regular courses about the non-euclidean geometries, based mainly on the Appendix. These lectures were published as a book in 1872 and 1876. Other events also drew the Hungarian mathematician's attention to the Bolyai-case. As a consequence, the idea was brought up for a second publication of the Tentamen and the Appendix, including the translation of the second one to Hungarian. A feverish activity began for the complete clarification of the area, which resulted in impressive transactions around the turn of the century.

Another precedent was the joining of G. B. Halsted (1853-1922), then professor of mathematics at the University of Austin, Texas to research done on absolute and hyperbolic geometry. His impartiality and familiarity with the area were quite important from the Hungarian point of view, as he considered it his task to achieve similar recognition throughout the world for János Bolyai and N. I. Lobachevski. It should be noted at this point that, till then, Lobachevski was more extensively commented upon and his treatises were more frequently published than those of Bolyai, because the Russians took more care of acknowledging their outstanding mathematician than we did with our János Bolyai. A statue was erected for him in Kazan and a generous award was established to honour his memory. Halsted commented this as follows (Science, New York, 20/12/1895):

"And precisely in that country, i. e. in Hungary, where János Bolyai's genius is so laudable in creating non-euclidean geometry, the Budapest Mathematical and Physical Society is content with having erected a memorial plaque onto the long ago collapsed grave in Marosvásárhely. "

In fact, the Mathematical-Physical Society of the Kazan University had established an international Lobachevski-prize in 1895, which was awarded every third year between 1899 and 1937 with some minor interruptions. Compared to the Bolyai-prize's regulations, there were some differences: e. g. an essential stipulation required, that the prize-winner's scientific pursuits should be connected with non-euclidean geometries. The first was given to Sophus Lie in recognition of his basic work on transformational groups.

Another event should be mentioned here: the establishment of the Nobel-prize on 20/11/1895. The prizes were first awarded at the end of 1901 and at the beginning there were 5 categories of prizes: physical, chemical, medical, literary, and peace prize. Later on there was much speculation about the omission of the mathematicians. Gösta Mittag-Leffler - the professor of the Stockholm University - might have had a role in it. (We will return to him from another aspect.) The point is, that he and his wife bequathed already on 6/1/1883 their villa in Djursholm to the Swedish Academy in the form of an international foundation. Their chief aim was to promote mathematical research in the Scandinavian countries.

Needless to say, the Hungarian scientists were aware of these events which preceded the centenary of János Bolyai's birth. The intention to rectify the negligence of earlier times by duly commemorating our world-famous mathematician became ever stronger. The idea of a large-scale celebration and of establishing an international Bolyai-award gradually became evident.

Finally, it is hard to decide which external factors from the above mentioned had the decisive influence on the establishing of a Bolyai-award. I don't think it likely that our scientists wanted to compete in any way with the Nobel-prize. It would have been beyond their financial means, although the 10,000 crown was a considerable sum yet still approximately one-tenth of the Nobel-prize. The key motives of our academicians could have been the Lobachevski-prize and the centenary of János Bolyai's birth.

If you turn over the pages of the academic publications, scientific journals or dailies of that period, it becomes evident from them, that the country embraced the idea enthusiastically. Our most prominent mathematicians and natural scientists drew up the award's regulations with great expertise.[3] - We could regard as a motto of recent researches, as well that sentence of the regulations which states the intention of the MTA, to erect by this decision a lasting memory of János Bolyai, "the immortal scientist, and of his deepthinking father, and master in science."

Many of the compilers of the regulations were thoroughly familiar with the content and value of the Tentamen and the Appendix as they took part in the preparations leading to the second publication of these works (Gyula Kőnig, Mór Réthy, József Kürschák, Béla Tőtössy and others).

It is not the intention of this article to give a detailed review of the regulations of the Bolyai-prize. However, as the original Hungarian version had been published in French and German, which were in turn sent to those academies having had considerable connections with the MTA, some differences among these versions would need an explanation.

The first of these is the title itself: Bolyai-award. The intention of the founders to acknowledge both the father and the son is conspicuous and noticeable from the wording of the regulations. Later on, the endowment became connected with the more significant of them: János Bolyai. During the translations "award" became "prize".

The regulations stipulated to take into consideration published treatises and books[4]. Still later some Hungarian report mentions written ones[5]. Certainly this is caused by an inaccurate quotation because at both occasions when the prize was in fact awarded, decisions were based on published works.

The regulations stipulate, that the decision should be taken by "a committee consisting of 2 internal and 2 external members" elected by the III. Department of the Academy. This could only mean, that 2 should be Hungarian members of the Academy and 2 external ones ("auswärtiger Mitglied", "membre étranger").

The Bolyai-prize was twice awarded: in 1905 and in 1910. At both occasions the committees acted in accordance with the above requirements. The Hungarian members of the committee at both occasions were Gyula Kőnig (ordinary member of the Academy from 1889) and Gusztáv Rados (corresponding member from 1894, ordinary member from 1907). In 1905 Gaston Darboux and Felix Klein were the committee's external members (elected by the Academy in 1902 and in 1899 respectively); in 1910 Gösta Mittag-Leffler and Henri Poincaré (elected in 1902 and in 1906 respectively). The winner in 1905 was Poincaré, in 1910 Hilbert: both became external members in 1906. The Bulletins of the Academy describe at length the conditions of the adjudgement of the Bolyai-prize, the course of the committee's sessions and "all the meetings" of the Academy in 1905 and in 1910, which was qualified to take the final decision according to the regulations. These reports give full details of the attentive work involved by the reception of the external committee-members, the compilation of the reports needed, and the notification of the known Hungarian and foreign mathematical journals and Academies.

The Bolyai-medal of the Hungarian Academy of Sciences

The planning and execution of the gold medal accompanying the prize was also a considerable task. The Academy's Archive of Manuscripts has in its possession almost 50 manuscripts and printed matter, which have something to do with the Bolyai-prize. From here, we know that the demanding execution of the medal was made excellently by István Schwartz (1851-1924), a sculptor and medal-artist of Hungarian origin, who lived and taught in Vienna (Fig. 1.). Unfortunately, we couldn't find the original medal, but we know of a bronze replica. I am indebted to academician Mihály Beck for a photo of it. The regulations put it this way: "One side of the medal is decorated by the picture of the MTA and Budapest, the other depicts a Hungarian inscription."[6]. We also know from the reports that in 1905 the committee had 2 candidates: Poincaré and Hilbert, supported equally. Finally Poincaré was chosen, but the decision requested the same appraisement for the 2 scientists in the minutes made for the presidency. The other point of interest is that in 1905 it was Felix Klein who should have assessed the 2 candidate's merits "for all the session" but because of his indisposition this difficult task fell upon Gusztáv Rados.

Felix Klein | Gaston Darboux | Gyula König | Gusztáv Rados
The Bolyai-award's committee in 1905

I also mention that Poincaré and Hilbert did not receive the award in Budapest: instead, it was delivered to them by official channels. As far as I know, Hilbert had never been to Budapest; Poincaré came here twice, but never in connection with the prize.

It is heart-warming to know, that the Bolyai-prize enjoyed a high reputation in the international scientific life. The reason was, that the 2 honoured men were in fact outstanding personalities in mathematics. The honoured mathematicians themselves felt highly esteemed being awarded the highest mathematical recognition of their times. To justify this, let me quote the grateful words of Hilbert:

"Ich bin um so mehr darauf stolz, als mir eine Auszeichnung so glänzender Art bisher nicht zu Teil geworden war." [7].

"I'm all the more proud of it, as up until now I have never been given such a distinctive honour."

Earlier a similar grateful letter arrived from Poincaré. We should attach a high value to these pronouncements, because in these years quite a few academies or universities elected them as external members or awarded them the honoris causa doctor title.

The Bolyai-award's committee in 1910.
From left to right: Gyula König, Gusztáv Rados, Henri Poincaré, Gösta Mittag-Leffler

All the data mentioned so far were more or less known, however, those enlisted below have been discovered quite recently - mainly by way of private correspondence and new research. E. g. it has been unclear, why the third Bolyai-prize (due in 1915, at the time of the I. World War) was not awarded.

Some treatises and books state, that Hilbert proposed Einstein in recognition of his role in creating the general theory of relativity. We know the origins of this statement; c. f. these lines from C. Reid: Hilbert (Springer, 1970, p. 142.):

"...when the time arrived for the awarding of the third Bolyai Prize in 1915, he recommended that it go to Einstein "for the high mathematical spirit behind all his achievements."

The point is, that the author does not give us the source of his claim. Neither the MTA's Archive of Manuscripts, nor the Hilbert-bequest in Göttingen contain any entry referring to Hilbert's initiative - as we shall have more to say about the latter. In the preface of his book C. Reid mentions by name approximately 20 mathematicians, who had personal contacts or correspondence with Hilbert. Thus it is quite possible, that the above mentioned information concerning Hilbert's recommendation influenced the author by private - oral or written - communication coming from this circle.

In order to settle the question I sent a letter to István Futaky, the retired director of the Finno-Ugrian Seminary of the Göttingen University. His thoroughness and readiness to help were touching, but still of no avail. However, it might be fitting to quote a part from professor Futaky's letter, although not directly connected with the Bolyai-prize. This is a handwritten draft from the Hilbert-bequest, dated 28/4/1906 and refers to the MTA as well:

"An die Akademien zu Budapest, Christiania, Kopenhagen: Hochgeehrter Herr Präsident. Von einer längeren Reise heimgekehrt, finde ich die Urkunde vor, die meine Ernennung zum auswärtigen Mitglied der Akademie ausspricht. Dieselbe ist mir eine ausserordentlich hohe Auszeichnung, über die ich eine grosse Freude empfinde und fűr die ich der hohen Akademie hiermit meinen herzlichsten Dank sage. Hochachtungsvoll Hilbert".

"To the Academies of Budapest, Christiana, Copenhagen: Dear Mr. President! Returning from a longer trip I received the document notifying me about my election to external membership of the Academy. This is a great honour for me and I would like to express my most cordial acknowledgements to the distinguished Academy. Respectfully yours Hilbert".

Obviously this is a common draft expression of thanks to the Hungarian, Norwegian and Danish Academies as they elected Hilbert to external membership.

According to the gracious communication of István Futaky all the documents relating to Hilbert were transferred at that time to the Archives of the Göttingen University Library. Unfortunately neither his election to external membership of the MTA, nor the Bolyai-prize has any trace in the collection, although many documents concerning acknowledgements, honorary doctorship are preserved in chronological order.

The efforts to find any relevant information in the bequest of Franz Hilbert (1893-1969), the last living son of Hilbert were also fruitless. This means, that we have no idea as to the origin of C. Reid's remark. Of course, one can still suppose, that not the complete Hilbert-bequest was transferred to the Göttingen University Library's Archives, or that some zealous researchers removed documents from it. Be as it may, any further research seems hopeless and there is little likelihood that Hilbert would have officially recommended Einstein to be awarded the Bolyai-prize in 1915. This is further supported by the earlier mentioned provision of the regulations, which allows to take into account only published works; however it was not earlier, than at the end of 1915, that Einstein presented his basic exposition of the general theory of relativity at the Berlin Academy, making use of the effective mathematical assistance of David Hilbert and his (Einstein's) collaborator of Hungarian origin, Marcel Grossmann (1878-1936) On the other hand, we have 2 letters in our possession showing, that despite the World War there was a keen interest in the Bolyai-prize in 1915. One was originated and the other was written by Gösta Mittag-Leffler (1846-1927); as we mentioned above, he was a foreign member of the prize-awarding committee.

The first letter was written "at the request of Mittag-Leffler" on 4/5/1915 by Marcell Riesz, then living in Stockholm to Lipót Fejér. A part of it goes like this:

Part of a letter of Gösta Mittag-Leffler to Lipót Fejér on 8/7/1915

"Mittag-Leffler would very much like to know, whether or not the Bolyai-prize will be awarded this year. If so, he would ask me to make confidential inquiries of you in order to know, whether he was again invited to the committee. It could be, that the point was not even brought up in Budapest, .... or, if it was, the members to be invited were not yet considered. He would be quite glad at being invited although, it is possible that those responsible might have decided otherwise... In his opinion, regarding either the actual merits or the political situation the prize this year should be given to a Hungarian mathematician. You know about his opinion concerning you. Lately he has had a high opinion of my brother too, due to the fact, that both Koch and Fredholm were absolutely delighted about Frici's book. "

Obviously the letter refers to Frigyes Riesz book: "Les systèmes d'équations linéaires à une infinité d'inconnues" published in Paris in 1913[8]. Helge von Koch (1870-1924) and Eric Fredholm (1866-1927) were excellent Swedish mathematicians.

Lipót Fejér's answer to Marcell Riesz letter was addressed directly to Mittag-Leffler. This follows clearly from Mittag-Leffier's answer sent during his Semmering summer holiday on 8/7/1915, in which he expresses his thanks to Lipót Fejér for his answer. We can only guess about the content of Fejér's letter, because it is not in our possession. He might have informed the Swedish mathematician, that due to the war's detrimental effects on international relations the MTA decided not to award the Bolyai-prize in 1915. Mittag-Leffler was understanding of the Academy's decision, but he was deeply concerned about the whole affair. To illustrate this and in conclusion let me quote 2 sentences from his letter mentioned above:

"... Sie in Ungarn schon so vorzügliches geleistet haben, dass es angemessen gewesen wäre den Preis an einem von Ihnen zu geben. Dies kann doch vielleicht das nächste Mal wenn der Preis verteilt wird, geschehen."

"...You in Hungary have already reached such extraordinary results, that it would be fitting if some of you would be awarded the prize. This could happen even at the next occasion, when the prize would be given."

We strongly hope, that at this time history would not prevent the renewal of the prize.

LITERATURE

(1) Akadémiai Hírek (Academic News) 1992/3, p. 9.
(2) Akadémiai Értesítő (Bulletin of the Academy) 1868, Vol. 2, p. 224.
(3) Akadémiai Értesítő (Bulletin of the Academy) 1903, Vol. 14, p. 111.
(4) Akadémiai Értesítő (Bulletin of the Academy) 1903, Vol. 14, p. 111.
(5) Akadémiai Értesítő (Bulletin of the Academy) 1911, Vol. 22, p. 49.
Math. Phys. Lapok (Mathematical and Physical Journal) 1911, Vol. 20, p. 2.
(6) Akadémiai Értesítő (Bulletin of the Academy) 1903, Vol. 14, p. 111.
(7) Hilbert's letter to Gusztáv Heinrich, in the MTA Library's Archive of Manuscripts.
(8) F. Riesz: Les systèmes d'équations linéaires à une infinité d'inconnues -
The linear systems of equations containing an infinite number of unknowns